The weighted Voronoi diagram and its applications in least-risk motion planning

Abstract

The authors present a path-planning algorithm to find the least-cost path along the WVD (weighted Voronoi diagram) based on Dijkstra's shortest path algorithm, where the cost of an edge is, in this case, the risk of transversing the edge. By imposing a discrete graph over the area of interest, the authors obtain a reduction from a continuous problem to a combinatorial problem. If the start or goal position does not lie on this graph, it is retracted by either the path of shortest distance or the path of steepest descent. Unfortunately, the WVD is not connected in some cases, and they have to enforce connectivity. With a practical aim in mind, the authors give a simple and easily computed path, connecting the disconnected components by the shortest distance path or by a circular path. With suitable preprocessing, they keep the run-time cost of path planning to O(n/sup 2/ log n), including the cost of retraction of both the start and goal positions and the cost of Dijkstra's shortest path (or least-cost) algorithm. The authors demonstrate a potential application of the weighted Voronoi diagram as a heuristic in least-risk motion planning. >